Class 11 Mathematics · Chapter 10 · Test 3
Double and Triple Angles
36 MCQs Covers double and triple angle formulas, numeric problems and proofs of identities. Also covers sin⁴θ in first powers and exact values of 18°, 36°, 54° and 72°.
36 questions · 30 min · 36 marks
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Sample questions
The first 5 of 36. Try each one, then tap to see the answer.
Question 1
sin 2α is equal to:
- Asin²α − cos²α
- B2 sin α cos α
- C2 sin α
- Dsin α + cos α
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Answer: B
Putting β = α in sin(α + β) = sin α cos β + cos α sin β gives sin 2α = 2 sin α cos α.
Question 2
Which of the following is NOT equal to cos 2α?
- Acos²α − sin²α
- B2 cos²α − 1
- C1 − 2 sin²α
- D1 − 2 cos²α
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Answer: D
cos 2α = cos²α − sin²α = 2cos²α − 1 = 1 − 2sin²α. The expression 1 − 2cos²α is not equal to cos 2α (it equals −cos 2α).
Question 3
tan 2α is equal to:
- A2 tan α/(1 − tan²α)
- B2 tan α/(1 + tan²α)
- C(1 − tan²α)/(2 tan α)
- Dtan α/(1 − tan²α)
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Answer: A
Putting β = α in tan(α + β) = (tan α + tan β)/(1 − tan α tan β).
Question 4
sin 3α is equal to:
- A4 sin³α − 3 sin α
- B3 sin α + 4 sin³α
- C3 sin α − 4 sin³α
- D3 cos α − 4 cos³α
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Answer: C
sin 3α = sin(2α + α) = sin 2α cos α + cos 2α sin α = 3 sin α − 4 sin³α.
Question 5
cos 3α is equal to:
- A3 cos α − 4 cos³α
- B4 cos³α − 3 cos α
- C4 cos³α + 3 cos α
- D3 sin α − 4 sin³α
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Answer: B
cos 3α = cos(2α + α) = cos 2α cos α − sin 2α sin α = 4cos³α − 3cos α.
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